# Rate of a Chemical Reaction

Rate of a Chemical Reaction

The rate of a chemical reaction is the change in the concentration of any one of the reactants or products per unit of time. It is expressed in mol L-1s-1 or Ms-1 or atm time-1 units.

it can be expressed in terms of:

(i) the rate of decrease in concentration of any one of the reactants, or

(ii) the rate of increase in concentration of any one of the products.

Consider a hypothetical reaction, assuming that the volume of the system remains constant.

R → P

One mole of the reactant R produces one mole of the product P. If [R]1 and [P]1 are the concentrations of R and P respectively at time t1 and [R]2 and [P]2 are their concentrations at time t2 then,

∆t = t2 – t1

∆[R] = [R]2 – [R]1

∆ [P] = [P]2 – [P]1

The square brackets in the above expressions are used to express molar concentration.

Rate of disappearance of R

(1)

Rate of appearance of P

(2)

Since ∆[R] is a negative quantity (as the concentration of reactants is decreasing), it is multiplied by –1 to make the rate of the reaction a positive quantity.

Equations (1) and (2) given above represent the average rate of a reaction, rav.

The average rate depends upon the change in concentration of reactants or products and the time taken for that change to occur.

Units of the rate of a reaction

From equations (1) and (2), it is clear that units of rate are concentration time–1. For example, if the concentration is in mol L–1 and time is in seconds then the units will be mol L-1s–1. However, in gaseous reactions, when the concentration of gases is expressed in terms of their partial pressures, then the units of the rate equation will be atm s–1.

For a chemical reaction,

Instantaneous Rate of Reaction

The rate of a chemical reaction at a particular moment of time is known as the instantaneous rate of reaction.

For reaction,

Now consider a reaction

Hg(l) + Cl2 (g)  HgCl2(s)

Where stoichiometric coefficients of the reactants and products are the same, then the rate of the reaction is given as

i.e., the rate of disappearance of any of the reactants is the same as the rate of appearance of the products. But in the following reaction, two moles of HI decompose to produce one mole each of H2 and I2,

2HI(g)  H2(g) + I2(g)

For expressing the rate of such a reaction where the stoichiometric coefficients of reactants or products are not equal to one, the rate of disappearance of any of the reactants or the rate of appearance of products is divided by their respective stoichiometric coefficients. Since rate of consumption of HI is twice the rate of formation of H2 or I2, to make them equal, the term [HI] is divided by 2. The rate of this reaction is given by

Rate of reaction

Similarly, for the reaction

5 Br- (aq) + BrO3 (aq) + 6 H+ (aq)  3 Br2 (aq) + 3 H2O (l)

For a gaseous reaction at a constant temperature, concentration is directly proportional to the partial pressure of a species, and hence, the rate can also be expressed as a rate of change in the partial pressure of the reactant or the product.

Factors Influencing Rate of a Reaction

1.     Nature and concentration of reactant

2.     Temperature

3.     Surface area of reactant

5.     Pressure of gas

Dependence of Rate on Concentration

Rate Expression and Rate Constant

Rate Law Expressions

Rate Law is the expression in which reaction rate is given in terms of molar concentration of reactant with each term raised to some Power, which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation

Rate Constant

In the above expression, k is called rate constant or velocity constant

Rate constant may be defined as the specific rate of reaction when the molar concentrations of the reactants is taken to be unity, i.e.,

Rate = k, if [A] = [B] = 1

Units of rate constant or specific reaction rate for a nth order reaction is given as

= (mol L-1)1-ns-1

Characteristics of rate constant

1     Greater the value of rate constant, faster is the reaction.

The value of rate constant for a reaction doesn’t depend upon the concentration of the reactants.

Order of a Reaction

Hence, the sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction.

Order of a reaction can be 0, 1, 2, 3 and even a fraction. A zero order reaction means that the rate of reaction is independent of the concentration of reactants.

A balanced chemical equation never gives us a true picture of how a reaction takes place since rarely a reaction gets completed in one step. The reactions taking place in one step are called elementary reactions. When a sequence of elementary reactions (called mechanism) gives us the products, the reactions are called complex reactions. These may be consecutive reactions (e.g., oxidation of ethane to CO2 and H2O passes through a series of intermediate steps in which alcohol, aldehyde and acid are formed), reverse reactions and side reactions (e.g., nitration of phenol yields o-nitrophenol and p-nitrophenol).

Units of rate constant

Units of rate constant

For a general reaction

aA + bB → cC + dD

Rate = k [A][B]y

Where x + y = n = order of the reaction

k =

Taking SI units of concentration, mol L–1 and time, s, the units of k for different reaction order are listed in Table

Molecularity of a Reaction

Another property of a reaction called molecularity helps in understanding its mechanism. The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called the molecularity of a reaction. The reaction can be unimolecular when one reacting species is involved, for example, the decomposition of ammonium nitrite.

NH4NO2  N2 + 2H2O

Bimolecular reactions involve simultaneous collision between two species, for example, dissociation of hydrogen iodide.

2HI  H2 + I2

Trimolecular or termolecular reactions involve simultaneous collision between three reacting species, for example,

2NO + O2  2NO2

The probability that more than three molecules can collide and react simultaneously is very small. Hence, reactions with the molecularity three are very rare and slow to proceed.

It is, therefore, evident that complex reactions involving more than three molecules in the stoichiometric equation must take place in more than one step.

KClO3 + 6FeSO4 + 3H2SO4  KCl + 3Fe2(SO4)+ 3H2O

This reaction which apparently seems to be of tenth order is actually a second-order reaction. This shows that this reaction takes place in several steps. Which step controls the rate of the overall reaction? The question can be answered if we go through the mechanism of reaction, for example, chances to win the relay race competition by a team depend upon the slowest person in the team. Similarly, the overall rate of the reaction is controlled by the slowest step in a reaction called the rate-determining step. Consider the decomposition of hydrogen peroxide which is catalysed by iodide ion in an alkaline medium.

2H2O2  2H2O + O2

The rate equation for this reaction is found to be

This reaction is first order with respect to both H2O2 and I. Evidences suggests that this reaction takes place in two steps

(1) H2O+ I–  H2O + IO

(2) H2O+ IO  H2O + I– + O2

Both steps are bimolecular elementary reactions. Species IO- is called an intermediate since it is formed during the course of the reaction but not in the overall balanced equation. The first step, being slow, is the rate-determining step. Thus, the rate of formation of the intermediate will determine the rate of this reaction.

Thus, from the discussion, till now, we conclude the following:

(i) The order of a reaction is an experimental quantity. It can be zero and even a fraction but molecularity cannot be zero or a non-integer.

(ii) Order is applicable to elementary as well as complex reactions whereas molecularity is applicable only for elementary reactions. For complex reactions, molecularity has no meaning.

(iii) For complex reactions, the order is given by the slowest step and the molecularity of the slowest step is the same as the order of the overall reaction.